We focus on the tools necessary for thinking like a mathematician. Students will learn to read proofs critically and to write
proofs rigorously. In addition, not only methods of proof, in this course, we review linear algebra and calculus.
Purpose of class
Successful students will be able to read proofs critically. Successful students will be able to write proofs rigorously. Successful students will gain deeper understanding of linear algebra and calculus.
Goals and objectives
Students will be able to read proofs critically.
Students will be able to write proofs rigorously.
Students will gain deeper understanding of linear algebra and calculus.
HW assignments (Including preparation and review of the class.)
Amount of Time Required
Proof by induction
Proof by contradiction
Review of linear algebra: vector spaces
Review of linear algebra: matrices
Review of linear algebra: diagonalization
Review of linear algebra: quadratic forms
Midterm examination and its review
Review of calculus: derivatives
Review of calculus: integrals
Review of calculus: partial derivatives
Review of calculus: double integrals
Final examination and its review
Relationship between 'Goals and Objectives' and 'Course Outcomes'
Evaluation method and criteria
Midterm exam and final exam 100%.
Textbooks and reference materials
Agata Stefanowicz, Proofs and Mathematical Reasoning. University of Birmingham, Mathematics support centre,